The technical community has long recognized the benefits of modeling and simulation as a major component of simulation systems, simulator systems, and embedded systems. Certain real-world activities, such as flight training, combat scenarios, missile operations, and fire fighting, are too expensive or too dangerous to test, practice, or use to support analytic studies. Modeling and simulation enables simulated testing, analysis, and personnel training without expending costly resources or exposing personnel to the dangerous situations.
Modeling provides a physical, mathematical, or logical representation of a system, entity, phenomenon, or process. An example of a model is an earth reference model (ERM), which provides a representation of certain aspects of the Earth, such as its shape, mass, and gravity. Simulation is a process of exercising a model over time. Categories of simulation include live simulation, virtual simulation, and constructive simulation. For live simulation, personnel use real-world equipment, such as airplanes, ships, missiles, and vehicles, which perform simulated operations, such as mock combat. For virtual simulation, personnel operate simulators instead of the actual real-world equipment. Constructive simulation involves computerized models of personnel and equipment that may have human interactors or players providing higher level tactics. The actions performed by the personnel and equipment modeled occur entirely within a computer program.
The usefulness of these types of simulations for testing, analyzing, or training depends upon how closely each simulation resembles the real world. The development of computational capabilities (e.g., more memory, faster processors and processing techniques) has improved the realism of some simulations. Yet despite this improvement, computational performance still limits the level of detail, and, thus, the degree of realism, attainable in simulation systems.
The coordinate framework used by a simulation system, for example, to simulate motion dynamics and geometric relations, is a principal factor in computational complexity. Computational complexity means that complex formulations are typically slower to compute than other formulations. Generally, the number of transcendental functions involved in a formulation provides a measure of the computational complexity of that formulation. Examples of transcendental functions include trigonometric functions, the inverse trigonometric functions and other functions such as powers, exponential functions, and logarithms.
Today, simulation systems use a variety of coordinate systems and associated earth reference models. Designers of these systems often assume that the earth is flat (locally) and use localized rectangular coordinates for both dynamic and static spatial referencing. The rectangular coordinates permit simplified mathematical formulation with the promise of acceptable computer runtimes. When employing rectangular coordinates, however, a designer of a typical, computationally intensive application involving Earth geometry makes major modeling compromises, such as gross simplifications to the actual shape of the Earth and to the local environment. These gross simplifications lead to a loss of fidelity that can endanger lives and require expensive subsequent reparations.
The Global Coordinate System (GCS) is an example of one such system that was designed to permit various simplifications to be made to increase processing speed, but such simplifications still compromise the fidelity of the underlying mathematical models. In GCS, the surface of the Earth Reference Model is divided (or tessellated) into nominally 1 degree latitude by 1 degree longitude cells (or tiles). A rectangular canonical local tangent plane (CLTP) coordinate system is defined at the center of each cell. One problem with GCS is that the latitude/longitude cells on the surface do not map to rectangles on each coordinate plane of the CLTP. Another problem is that the curved tessellation cell boundaries do not map to straight lines corresponding to rectangular cells. This introduces gaps or slivers in the surface representation. When the terrain surface is modeled in GCS, gaps may occur into which modeled entities such as vehicles can “disappear.” Such terrain skin representations can be repaired but at great expense and loss of fidelity.
In dynamic modeling within the GCS spatial framework, it is often assumed that the acceleration of gravity is normal (i.e., perpendicular) to the local tangent plane centered at the cell center. Because of this assumption, the acceleration of gravity is not normal to the Earth reference model for most points within the cell. This results in inaccurate dynamic formulations. Another simplification made when using GCS is that the vertical distance above each plane is deemed to be the same as geodetic height (height above an oblate spheroid). This simplification produces discontinuities across cell boundaries and modifies real world geometric relationships.
Therefore, there remains a need for a coordinate framework that reduces computational complexity yet avoids the aforementioned problems.